The present invention relates to a method and device for the treatment of biological samples using dielectrophoresis.
As is known, dielectrophoresis (DEP) is increasingly used in microchips to manipulate, identify, characterize and purify biological and artificial particles. DEP exploits frequency dependent differences in polarizability between the particles to be treated and the surrounding liquid that occur when RF (Radio Frequency) electric fields are applied thereto via microelectrodes.
In case of biological particles, to which reference is made without losing generality, the microelectrodes can additionally be used to apply DC (Direct Current) voltage pulses of high amplitude (of the order of 100 V) for short times (of the order of microseconds) to destroy membrane integrity of dielectrophoretically captured cells, for later PCR-Polymerase Chain Reaction (see, e.g., U.S. Pat. No. 6,280,590). On the other hand, solid-phase PCR (on-chip PCR) has been developed for later detection of products, e.g. in microarray format already commercially available [see, e.g., vbc-genomics.com/on_chip_pcr.html and WO-A-93/22058).
The theoretical background of DEP will be described herein below.
If a time-periodic electric field is applied to a dielectric particle, the particle is subject to a dielectrophoretic force that is a function of the dielectric polarizability of the particle in the liquid, that is the difference between the tendencies of particle and of the liquid to respond to the applied electrical field. In particular, for a spherical dielectric particle of radius R subject to an electric time-periodic field E having a root-mean-square value {right arrow over (E)}rms and angular frequency ω, the particle is subject to a dielectrophoretic force whose time averaged value {right arrow over (F)}dαν can be expressed using the dipole approximation as:
                                          〈                                          F                →                            d                        〉                    av                =                  2          ⁢                      πɛ            1                    ⁢                      R            3                    ⁢                      Re            ⁡                          [                              f                CM                            ]                                *                      ∇                                          E                →                            rms              2                                                          (        1        )            wherein ∈l is the liquid permittivity and fCM represents the above dielectric polarizability tendency, called the Clausius-Mossotti factor (see M. P. Hughes, Nanoelectromechanics in Engineering and Biology. 2002: CRC Press, Boca Raton, Fla. 322 pp). For a homogeneous sphere suspended in a liquid, the Clausius-Mossotti factor has been found to be:
                              f          CM                =                                                                                                  σ                    ~                                    p                                -                                                      σ                    ~                                    l                                                                                                  σ                    ~                                    p                                +                                  2                  ⁢                                                            σ                      ~                                        l                                                                        ⁢                                                  ⁢            with            ⁢                                                  ⁢                          σ              ~                                =                      σ            +            ⅈωɛ                                              (        2        )            wherein σ represents the conductivity (the index p referring to the particle and the index l referring to the liquid) and ∈ is the absolute permittivity.
For a more complex particle, the effective particle conductivity σ has to be used; e.g., in case of a particle with spherical shape, formed by a shell (membrane) enclosing a different material in the interior, it reads:
                                          σ            ~                    p                =                                            σ              ~                        m                    ⁢                      {                                                            a                  3                                +                                  2                  ⁢                                      (                                                                                                                        σ                            ~                                                    i                                                -                                                                              σ                            ~                                                    m                                                                                                                                                  σ                            ~                                                    i                                                +                                                  2                          ⁢                                                                                    σ                              ~                                                        m                                                                                                                )                                                                                                a                  3                                -                                  (                                                                                                              σ                          ~                                                i                                            -                                                                        σ                          ~                                                m                                                                                                                                      σ                          ~                                                i                                            +                                              2                        ⁢                                                                              σ                            ~                                                    m                                                                                                      )                                                      }                                              (        3        )            wherein the indices i and m refer to particle interior and membrane, respectively, and
  a  =      R          R      -      h      for a membrane with thickness h. R is again the particle radius.
FIG. 1 illustrates the relative dielectrophoretic force for lymphocytes (continuous line) and erythrocytes (broken lines) for media having three different conductivities. The dielectric spectra (ƒCM*R2) shifts to higher frequencies as conductivities rise and particles switch between positive DEP (pDEP, where the particles are attracted towards the electrodes), and negative DEP (nDEP, where the particles are repelled from the electrodes).
It has been already demonstrated (see Schnelle et al., “Paired microelectrode system: dielectrophoretic particle sorting and force calibration”, J. Electrostatics, 47/3, 121-132, 1999) that cells can be separated if they present different dielectrophoretic behaviour e.g. through different composition and/or size and/or shape, using equilibrium of flow (scaling with particle radius R) and DEP forces between face to face mounted electrode strips.
If a particle showing nDEP at preset conditions is brought by streaming near an energised electrode pair, it is lifted to the central plane, experiencing repulsion forces from both electrodes. FIG. 2 shows both equipotential and current lines between the electrode pair from the analytic solution for a semi-infinite plate capacitor.
Application of electric fields to conductive solutions is accompanied by heating. The balance equation for the temperature T reads:
                              ρ          ⁢                                          ⁢                                    c              p                        ⁡                          (                                                                    v                    →                                    ·                                      ∇                    T                                                  +                                                      ∂                                          ∂                      t                                                        ⁢                                                                          ⁢                  T                                            )                                      =                              λΔ            ⁢                                                  ⁢            T                    +                      σ            ⁢                                                  ⁢                          E              rms              2                                                          (        4        )            wherein ρ is the liquid density, cp is the specific heat, λ is the thermal conductivity and ν is the velocity of the liquid. For example, for water, cp=4.18 kJ/(kg K), λ˜0.6 W/(m K). If ρcpνα<<1, the flow term in eq. 4 can be neglected (v<<4 mm/s in a channel with a height a=40 μm) and eq. 4 can be simplified to:
                              ρ          ⁢                                          ⁢                      c            p                    ⁢                      ∂                          ∂              t                                ⁢          T                =                              λΔ            ⁢                                                  ⁢            T                    +                      σ            ⁢                                                  ⁢                          E              rms              2                                                          (        5        )            
The time constant td for thermal equilibrium can be derived to be:td=ρcpα2/λ  (6)which gives, for an aqueous solution and a=40 μm, td≅1 ms.
The stationary version of eq. 5 reads:0=λΔT+σE2  (7)
According to a dimensional analysis, this gives an order of magnitude estimate for the temperature rise of:∂T=σUrms2/λ  (8)wherein Urms is the root mean square voltage applied between the electrodes. For an aqueous solutions with σ=1 S/m and a root mean square voltage Urms=5 V, eq. (8) results in T≅42° C. Thus physiological solutions can be heated up to boiling using moderate voltages. The absolute value of temperature depends on the electric field distribution and geometry, and can be usually obtained using numerical procedures. Quantitatively temperature rise is given by:∂T=γσUrms2/λ  (8a)which wherein γ is a parameter depending on geometry of the system including the phase pattern of the voltage applied to electrodes.
In fact, eqs. (8) and (8a) underestimate the scaling at higher voltages. This is due to the fact the ohmic conductivity σ rises stronger then thermal conductivity λ:σ(∂T)=σ0(1+α∂T) α˜0.022/Kλ(∂T)=λ0(1+β∂T) β˜0.002/K  (9)
Taking eq. (9) into account, eq. (8a) results in:∂T(U)=γσ0/λ0U2(1+Γσ0/λ0(α−β)U2+O(U4))  (10)
Although eq. 10 is only strictly true for homogenous systems, it gives a good estimate for sandwich systems as well.
Based on the above, the object of the invention is to provide a highly efficient and low cost device and method for the manipulation of particles that allow reduction of overall diagnostic time and risk of contamination.